Over the past two decades several communication techniques, such as transmission schemes, have been developed that use multiple transmitters or transmit antennas and/or multiple receivers or receive antennas. The aim of these transmission schemes has been to achieve higher data transfer rates and/or higher reliability of the communication link between transmitter and receiver, especially in communication links with varying channels. These techniques are nowadays in widespread use and are essentially standards in different radio communication configurations.
One of these techniques, known as MIMO (multiple-input and multiple-output), typically consists of a system having t transmitters and r receivers. At a given time instant, the t transmitters send dependent or independent data (x1, x2, . . . , xt) simultaneously over a channel and in the same frequency band, thereby sending the data over a composite channel. The data may be modulated using an OFDM (orthogonal frequency-division multiplexing) scheme, whereby multiple symbols (i.e., data) can be modulated simultaneously over a plurality of sub-carriers and transmitted over a plurality of corresponding sub-channels. At the receiver end, r receivers (for example, receive antennas) are employed. The composite channel is characterized by an r×t channel transfer matrix H. Entries in such a matrix can be referenced as Hi,j, where each entry represents the transfer response from transmitter j to receiver i. In a MIMO-OFDM system, this configuration is used to characterize each one of the individual sub-carriers (i.e., the tones) such that the MIMO data is arranged in an orderly manner over the OFDM modulation. Such a configuration can be mathematically formalized by the following relation:y=Hx+n  (1)
where x is a transmit vector defined as x=[x1, x2, . . . , xt]T, y is a receive vector defined as y=[y1, y2, . . . , yr]T and n is a noise vector defined as n=[n1, n2, . . . , nr]T. In an expanded matrix form, Equation (1) can be rewritten as:
                                                        y              1                        =                                                            h                  11                                ·                                  x                  1                                            +                                                h                  12                                ·                                  x                  2                                            +              …              +                                                h                                      1                    ⁢                    t                                                  ·                                  x                  t                                            +                              n                1                                              ⁢                                          ⁢                      y            2                    =                                                    h                21                            ·                              x                1                                      +                                          h                22                            ·                              x                2                                      +            …            +                                          h                                  2                  ⁢                  t                                            ·                              x                t                                      +                          n              2                                      ⁢                                  ⁢        ⋮        ⁢                                  ⁢                              y            r                    =                                                    h                                  r                  ⁢                                                                          ⁢                  1                                            ·                              x                1                                      +                                          h                                  r                  ⁢                                                                          ⁢                  2                                            ·                              x                2                                      +            …            +                                          h                rt                            ·                              x                t                                      +                          n              r                                                          (        2        )            As shown in Equations (1) and (2), by traversing from the transmitter end to the receiver end, the independent signals {x1, x2, . . . , xt} are all combined in each one of the receivers. In order to recover each transmitted data stream {xj} from the received data streams {y1, y2, . . . , yr}, the channel matrix response is to be estimated and then Equations (1) and (2) are to be solved.
A variety of MIMO arrangements are known in the art. Such arrangements may differ in the number of transmit and receive ports. Two basic MIMO schemes currently used in communication systems are spatial multiplexing (herein abbreviated SM) and space-time transmit diversity (herein abbreviated STTD). In SM, independent data streams (i.e., spatial streams) are transmitted over different transmit ports and capacity gain is achieved. In STTD, in contrast to the SM scheme, the total number of transmit ports may surpass the total number of receive ports. In transmit diversity schemes (for example, beam-forming), a signal is transmitted redundantly through multiple transmit ports, thereby obtaining diversity gain and increased robustness of the communication link. In these schemes, a single spatial stream is mapped to multiple transmitters.
The basis for diversity gain in traditional receiver diversity schemes is that each receiver receives a different copy or combination of the transmitted signals. In wireless communication links, the probability that all of the received signals will experience high attenuation is considerably reduced. This diversity gain can also be achieved by employing multiple transmitters and repeating the same information from different transmitters as is done in space-time codes. These codes make the spatial diversity usable. In these codes, the redundant signal copies are transmitted not only from a different transmit port but also at a different time. Such coding schemes can also be applied in the frequency domain. The frequency domain counterpart to these coding schemes is called space-frequency coding. In a spatial multiplexing scheme however, MIMO arrangements are used to increase the spectral efficiency of the communication link instead of improving its robustness. An increase in spectral efficiency means an increase of the data transfer rate without consuming extra frequency bandwidth. In this scheme, multiple data streams, which originate from multiple independent data streams or from a single data stream divided into separate streams, are transmitted independently in parallel from the different transmitters. In general, there is an approximate linear increase in the achievable data transfer rate with every additional transmitter-receiver pair. Another MIMO scheme which is used in multi-user communication links, such as the uplink of cellular networks, is known as collaborative MIMO. In this scheme, multiple users collaboratively transmit over the same channel to a single destination.
In general, in order to maximize use of the channel capacity and enhance the robustness of a communications system, the transmitted signal should be adapted to the channel conditions. In one set of schemes, a receiver estimates the channel matrix response and channel state information. The receiver then may or may not convey the channel state information back to a transmitter via a special feedback channel. In a closed-loop MIMO arrangement, the channel state information is conveyed back to the transmitter, which enables the transmitter to respond to changing channel conditions and to modify the transmission of the transmitted signals. In an open-loop MIMO arrangement, the channel state information is not conveyed back to the transmitter. Another transmission scheme that attempts to maximize channel capacity is based on a closed-loop MIMO arrangement. In this scheme, the channel matrix response is transformed to its singular value decomposition. Based on this decomposition, the transmitter uses a substantially unitary precoder to transmit the signals which are derived from this matrix decomposition.
OFDM is a prevalent modulation scheme adopted by many state of the art communication standards. MIMO-OFDM systems combine the spectrally efficient OFDM modulation with a MIMO configuration in order to achieve a high communication system robustness or high data transfer rate. A MIMO-OFDM system transmits independent but synchronized OFDM symbols from different transmitters simultaneously. At the receiver, the MIMO decoding follows the OFDM modulation. In MIMO-OFDM schemes, the MIMO processing of the different sub-carriers in both the transmitter and receiver is accomplished independently of the other sub-carriers.